Material failure pervades the fields of materials science and engineering; it occurs at various scales and in various contexts. Understanding the mechanisms by which a material fails can lead to advancements in the way we design and build the world around us. For example, in structural engineering, understanding the fracture of concrete and steel can lead to improved structural systems and safer designs; in geological engineering, understanding the fracture of rock can lead to increased efficiency in oil and gas extraction; and in biological engineering, understanding the fracture of bone can lead to improvements in the design of bio-composites and medical implants. In this thesis, we numerically investigate a wide spectrum of failure behavior; in soft and quasi-brittle materials with nonhomogeneous microstructures considering a statistical distribution of material properties.
The first topic we investigate considers the influence of interfacial interactions on the macroscopic constitutive response of particle reinforced elastomers. When a particle is embedded into an elastomer, the polymer chains in the elastomer tend to adsorb (or anchor) onto the surface of the particle; creating a region in the vicinity of each particle (often referred to as an interphase) with distinct properties from those in the bulk elastomer. This interphasial region has been known to exist for many decades, but is primarily omitted in computational investigations of such composites. In this thesis, we present an investigation into the influence of interphases on the macroscopic constitutive response of particle filled elastomers undergoing large deformations. In addition, at large deformations, a localized region of failure tends to accumulate around inclusions. To capture this localized region of failure (often referred to as interfacial debonding), we use cohesive zone elements which follow the Park-Paulino-Roesler traction-separation relation. To account for friction, we present a new, coupled cohesive-friction relation and detail its formulation and implementation. In the process of this investigation, we developed a small library of cohesive elements for use with a commercially available finite element analysis software package.
Additionally, in this thesis, we present a series of methods for reducing mesh dependency in two-dimensional dynamic cohesive fracture simulations of quasi-brittle materials. In this setting, cracks are only permitted to propagate along element facets, thus a poorly designed discretization of the problem domain can introduce artifacts into the fracture behavior. To reduce mesh induced artifacts, we consider unstructured polygonal finite elements. A randomly-seeded polygonal mesh leads to an isotropic discretization of the problem domain, which does not bias the direction of crack propagation. However, polygonal meshes tend to limit the possible directions a crack may travel at each node, making this discretization a poor candidate for dynamic cohesive fracture simulations. To alleviate this problem, we propose two new topological operators. The first operator we propose is adaptive element-splitting, and the second is adaptive mesh refinement. Both operators are designed to improve the ability of unstructured polygonal meshes to capture crack patterns in dynamic cohesive fracture simulations. However, we demonstrate that element-splitting is more suited to pervasive fracture problems, whereas, adaptive refinement is more suited to problems exhibiting a dominant crack.
Finally, we investigate the use of geometric and constitutive design features to regularize pervasive fragmentation behavior in three-dimensions. Throughout pervasive fracture simulations, many cracks initiate, propagate, branch and coalesce simultaneously. Because of the cohesive element method's unique framework, this behavior can be captured in a regularized manner. In this investigation, unstructuring techniques are used to introduce randomness into a numerical model. The behavior of quasi-brittle materials undergoing pervasive fracture and fragmentation is then examined using three examples. The examples are selected to investigate some of the significant factors influencing pervasive fracture and fragmentation behavior; including, geometric features, loading conditions, and material gradation.